Probability Theory II

Welcome to Probability Theory II course home page. I am Siva Athreya the instructor for the course.

Schedule: Tuesday and Thursday: 9:55-10:55am and 2:00-3:00pm.

Location: Room G24, Main Building.

Syllabus:
Joint densities and distributions. Transformation of variables (assuming Jacobian formula). Distributions of sum, maxima, minima, order statistics, range etc. Multivariate normal (properties, linear combinations) and other standard multivariate distributions (discrete and continuous) as examples. Standard sampling distributions like t, chi-square, and F. Conditional distributions, Conditional Expectation. Characteristic functions: properties, illustrations, inversion formula, continuity theorem (without proof). Central Limit Theorem for i.i.d. case with finite variance. Elements of modes of convergence of random variables and the statement of the strong law of large numbers.


Homework :
Review of Probability 1
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8

References:

1. K. L. Chung: Elementary Probability Theory.
2. P. G. Hoel, S.C. Port and C.J. Stone : Introduction to Probability Theory.
3. R. Ash : Basic Probability Theory.
4. W. Feller : Introduction to Probability Theory and its Applications, Volume 1.
5. W. Feller : Introduction to Probability Theory and its Applications, Volume 2.
6. P. Billingsley : Probability and Measure.
7. V.K.Rohatgi: Probability theory.
8. Sheldon Ross: Introduction to Probability and Statistics for Engineers and Scientists

Scoring:
Final Exam is worth 50 %, Midterm is worth 30 % and Homework(s) and Quiz(es) are worth 20 %.



If you have any questions or comments about the class/webpage/or anything else you can visit me at
Room A12 , Main building
Stat-Math Unit
Indian Statistical Institute
Bangalore.

I can be reached via email at: athreyaATisibang.ac.in